Transcript Lecture 38-Revision

Revision of topics for
CMED 305 Final Exam
The exam duration: 1hour 30 min.
Marks :25
All MCQ’s.
You should choose the correct answer.
No major calculations, but simple maths IQ is required.
No need to memorize the formulas.
Bring your own calculator.
Cell phones are not allowed to use as a calculator.
Research Methodology:
Incidence and Prevalence (2)
Study Designs (Casecontrol, Cohort,Experimental,Cross sectional) (3)
Odds Ratio and Relative Risk (2)
Designing questionnaire and Study Tools for data collection (1)
Data Interpretation (2)
Biostatistics Topics: ( 40 questions)
1.
Sampling Techniques (4)
2.
Sample size (2)
3.
Type of data & graphical presentation(4)
4.
Summary and Variability measures (7)
5.
Normal distribution (2)
6.
Statistical significance using p-values (6)
7.
Statistical significance using confidence intervals (5)
8.
Statistical tests for quantitative variables (5)
9.
Statistical tests for qualitative variables (4)
10.
Spss software (1)
Probability Sampling
 Simple random sampling
 Stratified random
sampling
 Systematic random
sampling
 Cluster (area) random
sampling
 Multistage random
sampling
Non-Probability Sampling
 Deliberate (quota)
sampling
 Convenience sampling
 Purposive sampling
 Snowball sampling
 Consecutive sampling
Estimation of Sample Size by
Three ways:
By using
(1) Formulae (manual calculations)
(2) Sample size tables or Nomogram
(3) Softwares




Nominal – qualitative classification of
equal value: gender, race, color, city
Ordinal - qualitative classification which
can be rank ordered: socioeconomic
status of families
Interval - Numerical or quantitative data:
can be rank ordered and sizes compared :
temperature
Ratio - Quantitative interval data along
with ratio: time, age.
 QUALITATIVE
DATA (Categorical data)
 DISCRETE QUANTITATIVE
 CONTINOUS QUANTITATIVE
Categorical data
--- Bar diagram (one or two groups)
--- Pie diagram
Continuous data
--- Histogram
--- Frequency polygon (curve)
--- Stem-and –leaf plot
--- Box-and-whisker plot
--- Scatter diagram
Describing Data Numerically
Central Tendency
Quartiles
Variation
Shape
Arithmetic Mean
Range
Median
Interquartile Range
Mode
Variance
Geometric Mean
Standard Deviation
Skewness
Harmonic Mean
9
DISTRIBUTION OF DATA IS SYMMETRIC
---- USE MEAN & S.D.,
DISTRIBUTION OF DATA IS SKEWED
---- USE MEDIAN & QUARTILES(IQR)
 Bell-Shaped
(also
known as symmetric”
or “normal”)
 Skewed:


positively (skewed to the
right) – it tails off toward
larger values
negatively (skewed to the
left) – it tails off toward
smaller values
11
VARIANCE:
Deviations of each observation from the
mean, then averaging the sum of squares of
these deviations.
STANDARD DEVIATION:
“ ROOT- MEANS-SQUARE-DEVIATIONS”
 Standard
error of the mean (sem):
s
sx  sem 
n
 Comments:



n = sample size
even for large s, if n is large, we can get good
precision for sem
always smaller than standard deviation (s)

Standard error of mean is
calculated by:
s
sx  sem 
n
 Many

biologic variables follow this pattern
Hemoglobin, Cholesterol, Serum Electrolytes, Blood
pressures, age, weight, height
 One
can use this information to define what
is normal and what is extreme
 In clinical medicine 95% or 2 Standard
deviations around the mean is normal

Clinically, 5% of “normal” individuals are
labeled as extreme/abnormal

We just accept this and move on.
about mean, 
 Mean, median, and mode are equal
 Total area under the curve above the x-axis
is one square unit
 1 standard deviation on both sides of the
mean includes approximately 68% of the
total area
 Symmetrical


2 standard deviations includes approximately 95%
3 standard deviations includes approximately 99%
Measures of Position
z score
Sample
x
x
z= s
Population
x
µ
z=

Interpreting Z Scores
Unusual
Values
-3
Ordinary
Values
-2
-1
0
Z
Unusual
Values
1
2
3
Hypothesis
‘No difference ‘ or ‘No association’
Alternative hypothesis
Logical alternative to the null hypothesis
‘There is a difference’ or ‘Association’
simple, specific, in advance
Every decisions making process will commit two
types of errors.
“We may conclude that the difference is
significant when in fact there is not real
difference in the population, and so reject
the null hypothesis when it is true. This is
error is known as type-I error, whose
magnitude is denoted by the Greek letter ‘α’.
On the other hand, we may conclude that the
difference is not significant, when in fact
there is real difference between the
populations, that is the null hypothesis is not
rejected when actually it is false. This error
is called type-II error, whose magnitude is
denoted by ‘β’.
Disease (Gold Standard)
Absent
Present
Positive
Correct
Test
Result
False Positive
a
c
Negative
Total
False Negative
a+c
Total
a+b
b
d
Correct
b+d
c+d
a+b+c+d
Sampling
Investigation
P
S
S
Results
Inference
P value
Confidence intervals!!!
 This
level of uncertainty is called type 1
error or a false-positive rate (a)
 More commonly called a p-value
 In general, p ≤ 0.05 is the agreed upon level
 In other words, the probability that the
difference that we observed in our sample
occurred by chance is less than 5%

Therefore we can reject the Ho
Testing significance at 0.05 level
-1.96
Rejection
region
+1.96
Nonrejection region
Rejection
region
Za/2 = 1.96
Reject H0 if Z < -Z a/2 or Z > Z a/2
25
 Stating
the Conclusions of our Results
 When
the p-value is small, we reject
the null hypothesis or, equivalently, we
accept the alternative hypothesis.

“Small” is defined as a p-value  a, where a 
acceptable false (+) rate (usually 0.05).
 When
the p-value is not small, we
conclude that we cannot reject the
null hypothesis or, equivalently, there
is not enough evidence to reject the
null hypothesis.

“Not small” is defined as a p-value > a, where a =
acceptable false (+) rate (usually 0.05).
Estimation
Two forms of estimation
• Point estimation = single value, e.g., x-bar is
unbiased estimator of μ
• Interval estimation = range of values 
confidence interval (CI). A confidence
interval consists of:
Estimation Process
Population
Mean, , is
unknown
Sample
Random Sample
Mean
X = 50
I am 95%
confident that 
is between 40 &
60.
Different Interpretations of the 95% confidence
interval
• “We are 95% sure that the TRUE parameter
value is in the 95% confidence interval”
• “If we repeated the experiment many many
times, 95% of the time the TRUE parameter
value would be in the interval”
• “the probability that the interval would contain
the true parameter value was 0.95.”
Most commonly used CI:
CI 90% corresponds to p 0.10
CI 95% corresponds to p 0.05
CI 99% corresponds to p 0.01
Note:
p value  only for analytical studies
CI  for descriptive and analytical studies
CHARACTERISTICS OF CI’S
--The (im) precision of the estimate is
indicated by the width of the confidence
interval.
--The wider the interval the less precision
THE WIDTH OF C.I. DEPENDS ON:
---- SAMPLE SIZE
---- VAIRABILITY
---- DEGREE OF CONFIDENCE
Comparison of p values and
confidence interval
• p values (hypothesis testing) gives you the
probability that the result is merely caused by
chance or not by chance, it does not give the
magnitude and direction of the difference
• Confidence interval (estimation) indicates
estimate of value in the population given one
result in the sample, it gives the magnitude and
direction of the difference
Z-test:
Study variable: Qualitative
Outcome variable: Quantitative or Qualitative
Comparison: two means or two proportions
Sample size: each group is > 50
Student’s t-test:
Study variable: Qualitative
Outcome variable: Quantitative
Comparison: sample mean with population mean;
two means (independent samples); paired
samples.
Sample size: each group <50 ( can be used even for
large sample size)
Chi-square test:
Study variable: Qualitative
Outcome variable: Qualitative
Comparison: two or more proportions
Sample size: > 20
Expected frequency: > 5
Fisher’s exact test:
Study variable: Qualitative
Outcome variable: Qualitative
Comparison: two proportions
Sample size:< 20
Macnemar’s test: (for paired samples)
Study variable: Qualitative
Outcome variable: Qualitative
Comparison: two proportions
Sample size: Any
1. Test for single mean
2. Test for difference in means
3. Test for paired observation
Student ‘s t-test will be used:
--- When Sample size is small , for mean
values and for the following situations:
(1) to compare the single sample mean
with the population mean
(2) to compare the sample means of
two independent samples
(3) to compare the sample means of
paired samples

Statistical tests for qualitative
(categorical) data
When both the study variables and outcome
variables are categorical (Qualitative):
Apply
(i) Chi square test
(ii) Fisher’s exact test (Small samples)
(iii) Mac nemar’s test ( for paired samples)
Wishing all of you Best of
Luck !